Polarons and molecules in a two-dimensional Fermi gas

We study an impurity atom in a two-dimensional Fermi gas using variational wave functions for (i) an impurity dressed by particle-hole excitations (polaron) and (ii) a dimer consisting of the impurity and a majority atom. In contrast to three dimensions, where similar calculations predict a sharp transition to a dimer state with increasing interspecies attraction, we show that the polaron Ansatz always gives a lower energy. However, the exact solution for a heavy impurity reveals that both a two-body bound state and distortions of the Fermi sea are crucial. This reflects the importance of particle-hole pairs in lower dimensions and makes simple variational calculations unreliable. We show that the energy of an impurity gives important information about its dressing cloud, for which both Ansätze give inaccurate results.

Figure 1

Energy $E$ as a function of ${\epsilon }_B$ for the polaron Ansatz (for the $q=0$ approximation, see text) and the dimer Ansatz. For ${\epsilon }_B<2{\epsilon }_F$, the dimer has momentum $p_M\ne 0$; the thin straight line indicates the dimer energy at $p_M=0$.

Figure 2

Number of majority atoms $\nu$ in the dressing cloud of an impurity as a function of ${\epsilon }_B$.